Hi XXXXXXXXXX~
I have to agree with your vet's opinion that it will be fine for your pup to fly with a grade 3 murmur. At our practice, one of the techs has a Great Dane with a grade 5 (grades only go as high as 6) murmur and he flies all over with her whenever she goes on vacation without any problems.
More information on canine heart murmurs can be found here: http://dogs.lovetoknow.com/wiki/Canine_Heart_Murmur .
I hope this helps and I hope your pup enjoys his flight!
Certified Veterinary Technician
Associates Degree in Veterinary Technology. State and Nationally certified.